Maximum entropy on the mean approach to solve generalized inverse problems with an application in computational thermodynamics

Fabrice Gamboa (1) , Christine Gueneau (2) , Thierry Klein (3) , Eva Lawrence (2, 1, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire)
3 ENAC - Ecole Nationale de l'Aviation Civile

In this paper, we study entropy maximisation problems in order to reconstruct functions or measures subject to very general integral constraints. Our work has a twofold purpose. We first make a global synthesis of entropy maximisation problems in the case of a single reconstruction (measure or function) from the convex analysis point of view, as well as in the framework of the embedding into the Maximum Entropy on the Mean (MEM) setting. We further propose an extension of the entropy methods for a multidimensional case.

Mots clés: Entropy maximisation problems; Bayesian statistics; Application in Engineering Mathematics Subject Classification 90C25; 90C46; 62G07; 62P30

Domaines: Mathématiques [math]; Statistiques [math.ST]; Optimisation et contrôle [math.OC]

Fabrice Gamboa, Christine Gueneau, Thierry Klein, Eva Lawrence. Maximum entropy on the mean approach to solve generalized inverse problems with an application in computational thermodynamics. RAIRO - Operations Research, 2021, 55 (2), pp.355 - 393. ⟨10.1051/ro/2021005⟩. ⟨hal-02903231v1⟩